Calculus, integration problem??

Question

Hey, how can i integrate x/(1+(x^4))??? please help.

Answer 1

Put x = sqrt(t), so that dx = 1/(2 sqrt(t). Then,

Integral x/(1+(x^4) dx = Integral sqrt(t)/(1 + t^2) * 1/(2 sqrt(t) dt = (1/2) Integral dt/(1 + t^2) = (1/2) arctan(t) + C.

Since t = x^2, we finally have

Integral x/(1+(x^4) dx = (1/2) arctan(x^2) + C.